Detection Test for Periodic Signals Revisited Against Various Stochastic Models

Appropriate noise background should be taken into account when searching for the periodic or quasi-periodic oscillation buried in red noise. Null hypothesis assuming a conventional first-order autoregressive (AR(1)) process may lead to misleading conclusions since we know from many other studies that the noise in astrophysical and geographical sources exhibit the Fourier power-law-like properties. We improve the detection of periodic signals with the multitaper spectrum and wavelet spectrum by systematically taking into account a more appropriate null hypothesis (noise background) along with the multiple testing to test against. The confident level is determined with the noise contents obtained by using the maximum likelihood estimation (MLE) technique in the time domain, along with the data error covariance constructed using the fractional differencing. Not only traditional AR(1), but also the generalized Gauss-Markov, power law, and autoregressive fractionally integrated moving average (ARFIMA) process are included as possible candidate null hypothesis. The Bayesian Information Criterion (BIC) is adopted to quantify how well the candidate noise models fit the data under consideration. Our method is demonstrated on pre-seismic electromagnetic emissions, weight-percentage calcium carbonate data, and sea surface temperature anomaly variability. The result shows that our approach has a more extensive value of the application.